Answer:
155°
Step-by-step explanation:
The sum four angles is 360° so:
60°+45°+100°+x=360°
x = 360°-100°-45°-60°=155°
Multiple's of 5 are these:5<span>,10,15,20,25,30,35,40,45. :)</span>
The question is incomplete. Here is the complete question.
Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -
x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.
Answer: L = 1; W = 9/4; A = 2.25;
Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:
A = x.y
A = x(-
)
A = -
To maximize, we have to differentiate the equation:
=
(-
)
= -3x + 3
The critical point is:
= 0
-3x + 3 = 0
x = 1
Substituing:
y = -
x + 3
y = -
.1 + 3
y = 9/4
So, the measurements are x = L = 1 and y = W = 9/4
The maximum area is:
A = 1 . 9/4
A = 9/4
A = 2.25
<span>Using processing software (Excel) or even a decent scientific calculator. You input the values and generate the best fit cubic equation.
For number 1, the equation is
y = 8x10</span>⁻⁵ x³ - 0.0097 x² + 0.374 x + 1.083
where x is the number of years since 1900
y is the pounds cheese consumed
For number 2, the equation is
y = -3x10⁻⁵ x³ + 0.0028 x² + 0.2155 x + 1.7736
For number 3
P(-1) = 18
Answer:
See Explanation.
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra II</u>
- Log/Ln Property:

<u>Calculus</u>
Derivatives
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Chain Rule: ![\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Derivative of Ln: ![\frac{d}{dx} [ln(u)] = \frac{u'}{u}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bln%28u%29%5D%20%3D%20%5Cfrac%7Bu%27%7D%7Bu%7D)
Step-by-step explanation:
<u>Step 1: Define</u>

<u>Step 2: Differentiate</u>
- Rewrite:

- Rewrite [Ln Properties]:

- Differentiate [Ln/Chain Rule/Basic Power Rule]:

- Simplify:

- Rewrite:

- Combine:

- Reciprocate:

- Distribute:
